Convergence Rates

Abstract

For an ergodic Markov chain, one may take the value at a “large” time n, as a sample of the stationary distribution. The accuracy of the sample is measured in terms of the distance in variation between the sample and the target distribution. The following sections are devoted to the obtention of convergence speeds of an ergodic hmc to its stationary distribution, and in particular, of bounds of the second largest eigenvalue modulus of its transition matrix.